Summary 😎

This repository contains a code project I realized during my time at Code Chrysalis.
This project aims to demistify the RSA algorithm, or the idea of Public Key/Private Key concepts. In actual usage, for obvious security reasons, the numbers used are huge and as a result it is difficult to understand how things work.
I tried to implement by myself the RSA algorithm with small numbers, to try to understand how the model works below the hood.

Deployment 💾

This page is accessible on Github pages at the following address: https://alixfachin.github.io/easyCrypto/

Disclaimer ⚠️

Please kindly remember that this project is meant for teaching/understanding and as a result please do not use the results to encode sensitive information. I cannot be responsible for damage or negative outcomes following using this program with personal and/or sensitive information.

How to install 💻

• The package uses npm package manager.
• Download or clone the repository
• Run npm install
• Run npm run start to start the development server. You should be able to see the page with any browser on your localhost:3000 address.

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How to use the webpage 🤔

The page has two distinct parts:

• 🗝 Key Generator: to try to understand what is the principle used to find public and private keys.
• 🥷Encoding/Decoding: Once we have a public key/private key, we can put it in practice and encode/decode any message. (Without emojis, please.)

Description of the algorithm 🧑‍🔬

General considerations

A public key will in our case be a couple of integers (a,b).
The private key is constitued of another integer p, which, associated with the second key b makes the private key (p,b).

Coding and Encoding 📝

• We will transform characters into number, so we can assume that we want to transmit a sequence of numbers.
• In order to encode a character of code c, we take c to the power a.
  • The encoded character code will be the remainder of c^a by b, so (c^a mod b).
• In order to decode an encoded character, we can take the encoded character e and proceed with a similar operation, but this time with the private key p, i.e. e^p mod b.
• If we choose a,b and p wisely, we can assure that (c^a mod b)^p mod b = c so we have decoded the message.

Choosing the public and private keys 🔑

• As mentioned above, we need to choose a, b and p wisely, so that the operation works, but as well so that it is very difficult for anyone else to figure out p (the private key) while knowing a and b (which are public).
• Prime numbers have very interesting properties, and combining prime numbers with circular arithmetics ends up with such result.

If you want to know more 💪

I would recommend to look at the following videos:

• Introduction to RSA : Great pratical explanation from Eddie Woo
• Public key cryptography : Video from "the Art of the Problem"
• The Music of the Primes : Book by Marcus du Sautoy regarding Riemann's hypothesis.
• Udemy course about Number Theory and Cryptography

The following content is pretty math-heavy:

• Wikipedia page regarding Euler's theorem
• Brilliant page regarding Modular Arithmetic

Technologies used 🆙

• Using https://reactjs.org for front-end component and state management
• This project was bootstrapped with Create React App.
• Using JSBI for management of BigInt, necessary for mathematical computations but impossible to transpile for backward compatibility.
• Using https://fontflipper.com/upload to help choosing the fonts
• Using Unsplash to find background picture